We study fermion mass matrices of the cascade form which are compatible with the tri-bimaximal lepton mixing and generation mass hierarchy. The flat-cascade lepton matrices imply a parameter-independent relation among the mixing angles and mass eigenvalues. The relation has several indications that the atmospheric neutrino mixing angle is close to maximal and the other two angles have a correlation independently of neutrino mass eigenvalues. We also discuss phenomenological aspects of the cascade matrices; flavor-violating rare decays of charged leptons, thermal leptogenesis, and leptonic CP violation. Possible dynamical origins of the cascades are illustrated based on flavor symmetry and in higher-dimensional theory.
The neutrino oscillation data are well explained by the tri-bimaximal pattern. Recently it has been shown that also the bimaximal pattern could be a very good starting point in order to describe the lepton mixing. In this paper I review both the flavour structures and then I present an explicit example.
Inspired by the recent T2K indication of a relatively large theta_{13}, we provide a systematic study of some general modifications to three mostly discussed neutrino mixing patterns, i.e., tri-bimaximal, bimaximal and democratic mixing matrices. The correlation between theta_{13} and two large mixing angles are provided according to each modifications. The phenomenological predictions of theta_{12} and theta_{23} are also discussed. After the exclusion of several minimal modifications, we still have reasonable predictions of three mixing angles in 3 Sigma level for other scenarios.
Tri-bimaximal mixing is a specific lepton mixing ansatz, which has been shown to account very successfully for the established neutrino oscillation data. Working in a particular basis (the `circulant basis'), we identify three independent symmetries of tri-bimaximal mixing, which we exploit to set the tri-bimaximal hypothesis in context, alongside some simple, phenomenologically interesting CP-conserving and CP-violating generalisations.
We study a class of models for tri-bimaximal neutrino mixing in SO(10) grand unified SUSY framework. Neutrino masses arise from both type-I and type-II seesaw mechanisms. We use dimension five operators in order to not spoil tri-bimaximal mixing by means of type-I contribution in the neutrino sector. We show that it is possible to fit all fermion masses and mixings including also the recent T2K result as deviation from the tri-bimaximal.
We point out two simple but instructive possibilities to modify the tri-bimaximal neutrino mixing ansatz, such that leptonic CP violation can naturally be incorporated into the resultant scenarios of nearly tri-bimaximal flavor mixing. The consequences of two new ansaetze on solar, atmospheric and reactor neutrino oscillations are analyzed. We also discuss an interesting approach to construct lepton mass matrices under permutation symmetry, from which one may derive another nearly tri-bimaximal neutrino mixing scenario with no intrinsic CP violation in neutrino oscillations.
We propose an extension of tri-bimaximal mixing to include a non-zero reactor angle $θ_{13}$ while maintaining the tri-bimaximal predictions for the atmospheric angle $θ_{23}=45^o$ and solar angle $θ_{12}=35^o$. We show how such tri-bimaximal-reactor mixing can arise at leading order from the(type I) see-saw mechanism with partially constrained sequential dominance. Partially constrained sequential dominance can be realized in GUT models with a non-Abelian discrete family symmetry, such as $A_4$, spontaneously broken by flavons with a particular vacuum alignment.
Tri-bimaximal neutrino mixing may arise from see-saw models based on family symmetry which is spontaneously broken by flavons with particular vacuum alignments. However recent analyses hint that tri-bimaximal mixing may be insensitive to the precise form of vacuum alignment. In this paper we derive approximate analytic results which express the deviations from tri-bimaximal neutrino mixing due to vacuum misalignment. We also relate vacuum misalignment to departures from form dominance, corresponding to deviations from the real orthogonal $R$ matrix, where such corrections are necessary to allo…
Following recent results from the SNO solar neutrino experiment and the K2K long-baseline neutrino experiment, the combined existing data on neutrino oscillations now point strongly to a specific form for the lepton mixing matrix, with effective bimaximal mixing of $ν_μ$ and $ν_τ$ at the atmospheric scale and effective trimaximal mixing for $ν_e$ with $ν_μ$ and $ν_τ$ at the solar scale (hence `tri-bimaximal' mixing). We give simple mass-matrices leading to tri-bimaximal mixing, and discuss its relation to the Fritzsch-Xing democratic ansatz.
We show that in a recently proposed $S_3$ model for tri-bimaximal mixing pattern for neutrinos, CP violating phases in neutrino mixings are directly responsible for lepton asymmetry $ε_\ell$. In the exact tri-bimaximal limit, $ε_\ell$ is proportional to one of the Majorana phases whereas in the presence of small deviations from tri-bimaximal pattern, there are two contributions, one being proportional to the Dirac phase and the other to one of the two Majorana phases. In the second case, $θ_{13}$ is nonzero and correlated with the deviation from maximal atmospheric mixing.
We discuss a grand unified model based on SUSY SU(5) in extra dimensions and on the flavour group A4xU(1) which, besides reproducing tri-bimaximal mixing for neutrinos with the accuracy required by the data, also leads to a natural description of the observed pattern of quark masses and mixings.
The near maximal value for the atmospheric neutrino mixing angle together with the fact that the solar mixing angle satisfies the relation $\sin^2θ_\odot\simeq {1/3}$ is the basis for the so called tri-bimaximal mixing (tbm) when $θ_{13}=0$. In this note, we explore the possibility that tri-bimaximal mixing is an indication of a softly broken higher leptonic symmetry $S_3$, the permutation of three lepton families that embeds the $μ-τ$ exchange symmetry of leptons.
Recent results from T2K, MINOS and Double CHOOZ all indicate a sizeable reactor angle theta_13 which would rule out conventional tri-bimaximal lepton mixing. However, it is possible to maintain the tri-bimaximal solar and atmospheric mixing angle predictions, theta_12 ~ 35 degrees, theta_23 ~ 45 degrees even for a quite sizeable reactor angle theta_13 ~ 8 degrees, using an ansatz called tri-bimaximal-reactor (TBR) mixing proposed by one of us some time ago. We propose an explicit A4 model of leptons based on the type I seesaw mechanism at both the effective and the renormalisable level which, …
The tri-bimaximal mixing is a good approximation for the present data of neutrino mixing angles. The deviation from the tri-bimaximal mixing is discussed numerically in the framework of the A4 model. Values of \tan^2θ_{12}, \sin^2 2θ_{23} and |U_{e3}| deviate from the tri-bimaximal mixing due to the corrections of the vacuum alignment of flavon fields. It is remarked that \sin^2 2θ_{23} deviates scarcely from 1 while \sin^2θ_{12} can deviate from 1/3 considerably and \sinθ_{13} could be near the present experimental upper bound. The CP violating measure J_{CP} and the effective Majorana neutri…
We consider the perturbatively modified tribimaximal (or bimaximal) mixing to estimate the (Dirac-type) CP phase in neutrino mixing matrix. The expressions for the CP phase are derived from the equivalence between the standard parametrization of the neutrino mixing matrix for the Majorana neutrino and modified tribimaximal or bimaximal mixing matrices with appropriate CP phases. Carrying out numerical analysis based on the current experimental results for neutrino mixing angles, we can predict the values of the CP phase for several possible cases.
We study the phenomenological implications of breaking the Tri-Bimaximal (TBM) mixing in such a way that either first or second column of TBM mixing matrix remains invariant. We present two such textures and confront them with the experimental data. We give the predictions of these textures for atmospheric mixing angle $θ_{23}$ and Dirac-type CP violating phase $δ$ that will be measured in the future experiments.
An analysis of the leptonic texture for the new triangular mass matrices has been carried out. In particular, it is shown that both bimaximal and nearly bimaximal solutions for solar and atmospheric neutrino anomalies can be generated within this pattern. We have also derived exact and compact parametrization of the leptonic mixing matrix in terms of the lepton masses and the parameters $α, β'$ and $δ$. A consistency with the CHOOZ reactor result for $V_m{_{13}}$ and a smallness of the Jarlskog's invariant parameter are obtained.
We consider a model based on A4 semidirect product (Ze x Zmu x Ztau) flavor symmetry for Tri-Bimaximal lepton mixing with two scalar A4-triplets whose vacuum expectation values have the same alignment. Neutrino masses are generated through effective dimension five Weinberg operators. Charged leptons mass hierarchies are generated with an additional Froggatt-Nielsen U(1) flavor symmetry under which right-handed leptons are charged.
We propose a parametrization of the lepton mixing matrix in terms of an expansion in powers of the deviations of the reactor, solar and atmospheric mixing angles from their tri-bimaximal values. We show that unitarity triangles and neutrino oscillation formulae have a very compact form when expressed in this parametrization, resulting in considerable simplifications when dealing with neutrino phenomenology. The parametrization, which is completely general, should help to establish possible relations between the deviations of the reactor, solar and atmospheric mixing angles from their tri-bimax…
In models with flavour symmetries added to the gauge group of the Standard Model the CP-violating asymmetry necessary for leptogenesis may be related with low-energy parameters. A particular case of interest is when the flavour symmetry produces exact Tri-Bimaximal lepton mixing leading to a vanishing CP-violating asymmetry. In this paper we present a model-independent discussion that confirms this always occurs for unflavoured leptogenesis in type I see-saw scenarios, noting however that Tri-Bimaximal mixing does not imply a vanishing asymmetry in general scenarios where there is interplay be…
In this paper we study a parametrized description of neutrino mixing from a phenomenological point of view. We concentrate on the parametrization in terms of higher order corrections to the leading order mixing matrix. A method to describe subleading contributions and its applications to tri-bimaximal mixing are discussed. We show that mixing matrices similar to tri-bimaximal-Cabibbo mixing can be obtained by straightforward choices of parameters. To achieve better agreement with the experimental data without increasing the number of free parameters, we impose a simple phenomenological relatio…
General structures of the charged lepton and the neutrino mixing matrices leading to tri-bimaximal leptonic mixing are determined. These are then integrated into an SO(10) model within which detailed fits to fermion masses and mixing angles are given. It is shown that one can obtain excellent fits to all the fermion masses and quark mixing angles keeping tri-bimaximal leptonic mixing intact. Different perturbations to the basic structure are considered and those which can or which cannot account for the recent T2K and MINOS results on the reactor mixing angle $θ_{13}^l$ are identified.
It has recently been shown how tri-bimaximal neutrino mixing can be achieved, using the see-saw mechanism with constrained sequential dominance, through the vacuum alignment of a broken non-Abelian gauged family symmetry such as SO(3) or SU(3). Generalising the approach of Altarelli and Feruglio developed for an $A_4$ model we show how the reduction of the underlying symmetry to a discrete subgroup of SO(3) or SU(3) renders this alignment a generic property of such models. This means near tri-bimaximal mixing can be quite naturally accommodated in a complete unified theory of quark and lepton …
The tri-bimaximal mixing matrix is most likely the leading order term in the description of leptonic mixing. We derive deviations from tri-bimaximal mixing(TBM) due to corrections from the charged lepton sector. We assume a decoupled 2-3 symmetry, which is a $Z_2$ symmetry, in the charged lepton sector and another $Z_2$ symmetry in the neutrino sector. The TBM is obtained in the flavor symmetric limit. We consider deviations from the TBM form arising from the breaking of the 2-3 symmetry in the charged lepton sector but do not consider deviations from the breaking of the flavor symmetry in the…
We propose a scheme, based on Δ(27) flavor symmetry and supplemented by other discrete symmetries and inverse seesaw mechanism, where both the light neutrino masses and the deviation from tri-bimaximal mixing matrix can be linked to the source of lepton number violation. The hierarchies of the charged leptons are explained. We find that the quark masses including their hierarchies and the mixing can also be constructed in a similar way.
We examine relation between neutrino oscillation parameters and prediction of lepton flavor violation, in light of deviations from tri-bimaximal mixing. Our study shows that upcoming experimental searches for lepton flavor violation process can provide useful implications for neutrino mass spectrum and mixing angles. With simple structure of heavy right-handed neutrino and supersymmetry breaking sectors, the discovery of tau \to mu gamma decay determines neutrino mass hierarchy if large (order 0.1) reactor angle is established.
We show that the A4 discrete symmetry that naturally leads to tri-bimaximal neutrino mixing can be simply obtained as a result of an orbifolding starting from a model in 6 dimensions. This particular orbifolding has four fixed points where 4 dimensional branes are located and the tetrahedral symmetry of A4 connects these branes. In this approach A4 appears after the reduction from six to four dimensions as a remnant of the 6D space-time symmetry. A previously discussed supersymmetric version of A4 is reinterpreted along these lines.
We postulate that the neutrino mass matrix in the lepton flavour basis is an S3 group matrix in the natural representation of S3. This immediately requires one neutrino to be trimaximally mixed, as suggested by the solar neutrino data. We go on to postulate that the charged-lepton mass matrix in the neutrino mass-basis is an S3 class matrix in the natural representation of the S3 class-algebra, leading to exact tri-bimaximal mixing, which is compatible with data overall. The tri-bimaximal mixing matrix is seen to be closely related to the S3 character table, and is properly the S2 C S3 table o…
We show that the next-to-leading order corrections in the quark-lepton complementarity are important to explain the observed pattern of neutrino mixing. In particular, the next-to-leading order corrections 1) lead to a deviation of θ_{23} from maximal mixing, 2) reduce the predicted value of $\sin^2 2θ_{13}$ by 9.8%, 3) provide the same value of $\sin^2 θ_{12}$ as that of the tri-bimaximal mixing. This is shown by calculating $\sin^2 2θ_{ij} (i,j=1,2,3)$ to ${\cal O}(λ^6)$ in the framework in which the product of the CKM and PMNS matrices is bimaximal.
We propose a realization of the so-called bimodal/schizophrenic model proposed recently. We assume S4, the permutation group of four objects as flavor symmetry giving tri-bimaximal lepton mixing at leading order. In these models the second massive neutrino state is assumed quasi-Dirac and the remaining neutrinos are Majorana states. In the case of inverse mass hierarchy, the lower bound on the neutrinoless double beta decay parameter m_ee is about two times that of the usual lower bound, within the range of sensitivity of the next generation of experiments.
We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies are determined by the $A_4\times Z_4$ flavour symmetry itself without invoking a Froggatt-Nielsen U(1) symmetry. Tri-Bimaximal mixing is exact in leading order while all the mixing angles receive corrections of the same order in next-to-the-leading approximation. As a consequence the predicted value of $θ_{13}$ is within the sensitivity of the experiments whic…
The A4 group stands in the basis of many models that predict Tri-Bimaximal neutrino mixing at leading order. We study the Altarelli-Feruglio A4 symmetry model and show that in order to produce as small value of r_{23} (ratio of mass-squared differences) as measured, it requires fine tuning. This observation is important for an evaluation of the model, since the problem it is trying to solve in the first place is the tuning of the three mixing angles. We get the required level of fine tuning for the model in both its basic form and its seesaw realization.
The tetrahedron $A_4$ group has been widely used in studying neutrino mixing matrix. It provides a natural framework of model building for the tri-bimaximal mixing matrix. In this class of models, it is necessary to have two Higgs fields, $χ$ and $χ'$, transforming under $A_4$ as 3 with one of them having vacuum expectation values for the three components to be equal and another having only one of the components to be non-zero. These specific vev structures require separating $χ$ and $χ'$ from communicating with each other. The clash of the different vev structures for $χ$ and $χ'$ is the so c…
We determine the symmetry groups under which the charged-lepton and the Majorana-neutrino mass terms are invariant. We note that those two groups always exist trivially, i.e. independently of the presence of any symmetries in the Lagrangian, and that they always have the same form. Using this insight, we re-evaluate the recent claim that, whenever lepton mixing is tri-bimaximal, S_4 is the minimal unique horizontal-symmetry group of the Lagrangian of the lepton sector, with S_4 being determined by the symmetries of the lepton mass matrices. We discuss two models for tri-bimaximal mixing which …
We study perturbations of exactly tri-bimaximal neutrino mixings under the assumption that they are coming solely from the charged lepton mass matrix. This may be plausible in scenarios where the mass generation mechanisms of neutrinos and charged leptons/quarks have a different origin. As a working hypothesis, we assume mass textures which may be generated by the Froggatt-Nielsen mechanism for the charged lepton and quark sectors, which generically leads to strong hierarchies, whereas the neutrino sector is exactly tri-bimaximal with a mild (normal) hierarchy. We find that in this approach, d…
We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from th…
We model tri-bimaximal lepton mixing from first principles in a way that avoids the problem of the vacuum alignment characteristic of such models. This is achieved by using a softly broken A4 symmetry realized with an isotriplet fermion, also triplet under A4. No scalar A4-triplet is introduced. This represents one possible realization of general schemes characterized by the minimal set of either three or five physical parameters. In the three parameter versions mee vanishes, while in the five parameter schemes the absolute scale of neutrino mass, although not predicted, is related to the two …
We present a supersymmetric $T_{13}$ model for the tri-bimaximal neutrino mixing, and the complete flavor group is $T_{13}\times Z_{4}\times Z_2$. At leading order, the residual symmetry of the charged lepton sector is $Z_3$, and the $T_{13}$ symmetry is broken completely in the neutrino sector. The charged lepton mass hierarchies are determined by the spontaneous breaking of the flavor symmetry, both the type I see-saw mechanism and the Weinberg operator contribute to generating the light neutrino masses. Tri-bimaximal mixing is exact at leading order while subleading contributions introduce …
Bimaximal (BM) and tri-bimaximal (TB) mixings of neutrinos are two special cases of lepton mixing matrix, which predict the reactor angle $θ_{13}=0$ and the atmospheric angle $\tan^2θ_{23}=1$. Recent precision measurements and global analysis of oscillation parameters, have confirmed a non-vanishing value of $θ_{13}$ as well as deviations of $θ_{12}$ and $θ_{23}$ from their maximal values predicted by BM or TB mixing. In this work we mainly concentrate on $θ_{13}$ and $θ_{23}$ to assign $\sinθ_{13}\neq 0$ and $\tan^2θ_{23}<1$ with the help of charged lepton corrections defined by $U_{PMNS}=U^{…
In this paper, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group $S4$ as the family symmetry. In order to constrain the form of superpotential, a $Z3$ symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of $\mathcal{O}(0.01)$ at NLO. The mechanism to get the partic…
We analyze the effects of charged lepton corrections and renormalization group (RG) running on the low energy predictions of theories which accurately predict tri-bimaximal neutrino mixing at the high energy scale. In particular we focus on GUT inspired see-saw models with accurate tri-bimaximal neutrino mixing at the GUT scale, in which the charged lepton corrections are Cabibbo-like and give rise to sum rules valid at the GUT scale. We study numerically the RG corrections to a variety of such neutrino mixing sum rules in order to assess their accuracy and reliability when comparing them to f…
We introduce a small correction term, δM_ν, in the neutrino sector and examine whether a large θ_13 and an almost maximal θ_23 can simultaneously be obtained starting from the tri-bimaximal neutrino mixing. It is found that one can easily gain θ_13 \simeq 10^\circ, which is favored by the recent T2K experiment, by taking account of the enhancement due to the degeneracy among three neutrino masses. We also find that (δM_ν)_22=(δM_ν)_33 is a key condition for θ_23 \simeq 45^\circ.
The recent results from T2K and MINOS experiments point towards a relatively large value of the reactor angle θ_13 in the lepton sector. In this paper we show how a large θ_13 can arise from the charged lepton sector alone in the context of an SU(5) GUT. In such a scenario (tri-)bimaximal mixing in the neutrino sector is still a viable possibility. We also analyse the general implications of the considered scenario for the searches of CP violation in neutrino oscillations.
In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these ra…
We investigate the Friedberg-Lee (FL) symmetry and its promotion to include the $μ- τ$ symmetry, and call that the twisted FL symmetry.Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we suggest the semi-uniform translation of the FL symmetry.The second one is based on the $S_3$ permutation family symmetry.The breaking terms, which are twisted FL symmetric, are introduced.Some viable models in each scheme are also presented.
Recent measurements of the lepton mixing angle $θ_{13}$ by the Daya Bay and RENO reactor experiments are consistent with the relationship $θ_{13}\approx θ_C/\sqrt{2}$ where $ θ_C$ is the Cabibbo angle. We propose Tri-bimaximal-Cabibbo (TBC) mixing, in which $\sin θ_{13}= \sin θ_C/\sqrt{2}$, $\sin θ_{23}= 1/\sqrt{2}$ and $\sin θ_{12}= 1/\sqrt{3}$. We show that TBC mixing may arise approximately from Tri-bimaximal, Bi-maximal or Golden Ratio neutrino mixing, together with Cabibbo-like charged lepton corrections arising from a Pati-Salam gauge group, leading to predictions for the CP-violating ph…
We present a tri-bimaximal lepton mixing scheme where the neutrinoless double beta decay rate (bb0v) has a lower bound which correlates with the ratio alpha = Dmsol/Dmatm well determined by current data, as well as with the unknown Majorana CP phase phi12 characterizing the solar neutrino sub-system. For the special value phi12 = pi/2 (opposite CP-sign neutrinos) the bb0v rate vanishes at tree level when Dmsol/Dmatm = 3/80, only allowed at 3 sigma. For all other cases the rate is nonzero, and lies within current and projected experimental sensitivities close to phi12=0. We suggest two model re…
We present a type-III version of inverse seesaw or, equivalently an inverse version of type-III seesaw. Naturally small neutrino masses arise at low-scale from the exchange of neutral fermions transforming as hyperchargeless SU(2) triplets. In order to implement tri-bimaximal lepton mixing we supplement the minimal SU(3)xSU(2)xU(1) gauge symmetry with an A4-based flavor symmetry. Our scenario induces lepton flavour violating (LFV) three body decays that can proceed at the tree level, while radiative li to lj gamma decays and mu-e conversion in nuclei are also expected to be sizeable. LFV decay…
We construct a model for tri-bimaximal lepton mixing which employs only family symmetries and their soft breaking; neither vacuum alignment nor supersymmetry, extra dimensions, or non-renormalizable terms are used in our model. It is an extension of the Standard Model making use of the seesaw mechanism with five right-handed neutrino singlets. The scalar sector comprises four Higgs doublets and one complex gauge singlet. The horizontal symmetry of our model is based on the permutation group S_3 of the lepton families together with the three family lepton numbers--united this constitutes a symm…
We analyze in detail the predictions of "trimaximal" neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually have the same forms as for tri-bimaximal mixing. The phenomenology of these new mixing scenarios is studied. We emphasize how trimaximal mixings can be distinguished experimentally from broken tri-bimaximal mixing.
We have studied the contribution of higher order corrections of the flavor symmetry breaking in the $A_4$ seesaw model with the supersymmetry. Taking account of possible higher dimensional mass operators, we predict the deviation from the tri-bimaximal lepton mixing for both normal hierarchy and inverted hierarchy of neutrino masses. We have found that the value of $\sin^2 2θ_{23}$ is larger than 0.96 and the upper bound of $\sin^2θ_{13}$ is 0.01. We have also examined the flavor changing neutral current of leptons from the soft SUSY breaking in slepton masses and A-terms within the framework …
We consider tri-bimaximal lepton mixing within low-scale seesaw schemes where light neutrino masses arise from TeV scale physics, potentially accessible at the Large Hadron Collider (LHC). Two examples are considered, based on the A4 flavor symmetry realized within the inverse or the linear seesaw mechanisms. Both are highly predictive so that in both the light neutrino sector effectively depends only on three mass parameters and one Majorana phase, with no CP violation in neutrino oscillations. We find that the linear seesaw leads to a lower bound for neutrinoless double beta decay while the …
We investigate deviation from the tri-bimaximal mixing in the case of ultra high energy neutrino using ICECUBE detector. We consider the ratio of No. of muon tracks to the shower generated due to eletrons and hadrons. Our analysis shows for tri-bimaximal mixing the ratio comes out around 4.05. Keeping $θ_12$ and $θ_23$ fixed at tri-bimaximal value, we have varied the angle $θ_{13}$ = $3^o$, $6^o$, $9^o$ and the value of the ratio gradually decreases. The variation of ratio lies 8% to 18% from the tri-bimaximal mixing value.
In this note I mainly focus on the neutrino physics part in my talk and report the most recent progress made in \cite{YLW0}. It is seen that the Majorana features of neutrinos and SO(3) gauge flavor symmetry can simultaneously explain the smallness of neutrino masses and nearly tri-bimaximal neutrino mixing when combining together with the mechanism of approximate global U(1) family symmetry. The mixing angle $θ_{13}$ and CP-violating phase are in general nonzero and testable experimentally at the allowed sensitivity. The model also predicts the existence of vector-like Majorana neutrinos and …
Current data indicates that lepton mixing is very close to the tri-bimaximal mixing scenario. In general, however, one expects deviations from any mixing scenario. We discuss several examples to perturb tri-bimaximal mixing, namely soft breaking, renormalization group running and charged lepton corrections. We also present a convenient parametrization of the PMNS matrix which takes advantage of the apparently close to tri-bimaximal mixing pattern. Finally, it is discussed how to generate values of U_{e3} which correspond to the recently found hint for non-zero U_{e3}.
The long baseline neutrino experiment, T2K, and the reactor experiment, Double Chooz will soon present new data. If we expect $\sinθ_{13}$ to be 0.1-0.2, which is close to the present experimental upper bound, we should not persist in the paradigm of the tri-bimaximal mixing. We discuss breaking the tri-bimaximal mixing by adding a simple mass matrix, which could be derived from some non-Abelian discrete symmetries. It is found that $\sinθ_{13}=0.1-0.2$ is expected in our model independent analysis of the generalized mass matrix for the normal or inverted hierarchical neutrino mass spectrum. O…
We propose a new pattern of the neutrino mixing matrix which can be parametrized as the product of an arbitrary Hermitian matrix and the well-known tri-bimaximal mixing matrix. In this scenario, nontrivial values of the smallest neutrino mixing angle θ_13 and the CP-violating phases entirely arise from the non-unitary corrections. We present a complete set of series expansion formulas for neutrino oscillation probabilities both in vacuum and in matter of constant density. We do a numerical analysis to show the non-unitary effects on neutrino oscillations. The possibility of determining small n…
We discuss consequences of combining the effective $Z_2\times Z_2$ symmetry of the tri-bimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized $Z_2\times Z_2$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to non-zero $θ_{13}$ and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized $Z_2\times Z_2$ symmetry of the mass matrix can arise from the $A_4$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real pa…
It is well known that the tri-bimaximal neutrino mixing pattern V_0 can be derived from a class of flavor models with the non-Abelian A_4 symmetry. We point out that small corrections to V_0, which are inherent in the A_4 models and arise from both the charged-lepton and neutrino sectors, have been omitted in the previous works. We show that such corrections may lead the 3 \times 3 neutrino mixing matrix V to a non-unitary deviation from V_0, but they cannot result in a nonzero value of θ_13 or any new CP-violating phases. Current experimental constraints on the unitarity of V allow us to cons…
We review the application of non-Abelian discrete groups to Tri-Bimaximal (TB) neutrino mixing, which is supported by experiment as a possible good first approximation to the data. After summarizing the motivation and the formalism, we discuss specific models, mainly those based on A4 but also on other finite groups, and their phenomenological implications, including the extension to quarks. The recent measurements of θ_13 favour versions of these models where a suitable mechanism leads to corrections to θ_13 that can naturally be larger than those to θ_12 and θ_23. The virtues and the problem…
In view of the recent neutrino oscillation data pointing to a non-vanishing value for the smallest mixing angle ($θ_z$), we derive and find explicit realizations of the $(Z_2)^3$ flavor symmetry which characterizes, for the neutrino mass matrix, uniquely a variant of the tripartite form, originally conceived to lead to the tri-bimaximal mixing with $θ_z=0$, so that to allow now for a non-tri-bimaximal pattern with non-zero $θ_z$. We impose this flavor symmetry in a setting including the charged leptons and we see that it can make room, through higher order terms involving new SM-singlet scalar…
